3 research outputs found
Kernel-based Impulse Response Identification with Side-Information on Steady-State Gain
In this paper, we consider the problem of system identification when
side-information is available on the steady-state (or DC) gain of the system.
We formulate a general nonparametric identification method as an
infinite-dimensional constrained convex program over the reproducing kernel
Hilbert space (RKHS) of stable impulse responses. The objective function of
this optimization problem is the empirical loss regularized with the norm of
RKHS, and the constraint is considered for enforcing the integration of the
steady-state gain side-information. The proposed formulation addresses both the
discrete-time and continuous-time cases. We show that this program has a unique
solution obtained by solving an equivalent finite-dimensional convex
optimization. This solution has a closed-form when the empirical loss and
regularization functions are quadratic and exact side-information is
considered. We perform extensive numerical comparisons to verify the efficiency
of the proposed identification methodology
Kernel-Based Identification with Frequency Domain Side-Information
In this paper, we discuss the problem of system identification when frequency
domain side information is available on the system. Initially, we consider the
case where the prior knowledge is provided as being the \Hcal_{\infty}-norm
of the system bounded by a given scalar. This framework provides the
opportunity of considering various forms of side information such as the
dissipativity of the system as well as other forms of frequency domain prior
knowledge. We propose a nonparametric identification method for estimating the
impulse response of the system under the given side information. The estimation
problem is formulated as an optimization in a reproducing kernel Hilbert space
(RKHS) endowed with a stable kernel. The corresponding objective function
consists of a term for minimizing the fitting error, and a regularization term
defined based on the norm of the impulse response in the employed RKHS. To
guarantee the desired frequency domain features defined based on the prior
knowledge, suitable constraints are imposed on the estimation problem. The
resulting optimization has an infinite-dimensional feasible set with an
infinite number of constraints. We show that this problem is a well-defined
convex program with a unique solution. We propose a heuristic that tightly
approximates this unique solution. The proposed approach is equivalent to
solving a finite-dimensional convex quadratically constrained quadratic
program. The efficiency of the discussed method is verified by several
numerical examples
A Robust Multilabel Method Integrating Rule-based Transparent Model, Soft Label Correlation Learning and Label Noise Resistance
Model transparency, label correlation learning and the robust-ness to label
noise are crucial for multilabel learning. However, few existing methods study
these three characteristics simultaneously. To address this challenge, we
propose the robust multilabel Takagi-Sugeno-Kang fuzzy system (R-MLTSK-FS) with
three mechanisms. First, we design a soft label learning mechanism to reduce
the effect of label noise by explicitly measuring the interactions between
labels, which is also the basis of the other two mechanisms. Second, the
rule-based TSK FS is used as the base model to efficiently model the inference
relationship be-tween features and soft labels in a more transparent way than
many existing multilabel models. Third, to further improve the performance of
multilabel learning, we build a correlation enhancement learning mechanism
based on the soft label space and the fuzzy feature space. Extensive
experiments are conducted to demonstrate the superiority of the proposed
method.Comment: This paper has been accepted by IEEE Transactions on Fuzzy System